Extremal black hole mimickers: geometry, stability, and long-delay signal trains
Abstract
We present a spacetime that serves as a horizonless mimicker of extremal black holes. Unlike previously studied mimickers of black holes with non-degenerate horizons, whose geometries are of the wormhole type and consist of two asymptotically flat regions connected by a very long throat, the mimicker of an extremal black hole possesses a single asymptotically flat region at one end and an infinitely long throat at the other. In the throat region, the spacetime approaches the direct-product geometry M1,1 × S2, where M1,1 is two-dimensional Minkowski spacetime and S2 is the two-sphere. We investigate scalar-field dynamics and the fate of the Aretakis instability. Although Aretakis-like modes arise in a local analysis of the throat, they do not lead to a physical instability of the mimicker. A scalar perturbation initially localized in the throat gives rise, at late times, to a sequence of signals with a characteristic separation tdelay∼ 1/λ, where λ≪ 1 is a deformation parameter. This timescale is parametrically larger than the echo time techo∼ ln(1/λ) characteristic of non-extremal black-hole mimickers. We refer to this sequence as a {\it long-delay signal train}. Geometrically, the periodicity of the long-delay signals is associated with periodic geodesics on S2. We then extend the construction to extremal Kerr. In this case, the throat region approaches a generalized product geometry involving M1,1 and a two-dimensional surface Σ2. The corresponding signals are expected to form a quasi-periodic signal train, reflecting the quasi-periodic geodesic motion on Σ2. We also comment on the generalization to wormhole mimickers of non-extremal black holes and on the implications of these results for unitarity in the context of the AdS/CFT correspondence.
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BibTeX
@misc{solodukhin2026extremal,
title = {{Extremal black hole mimickers: geometry, stability, and long-delay signal trains}},
author = {Sergey N Solodukhin},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11664},
eprint = {2610.11664},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05835182v1},
}
RIS
TY - UNPB
TI - Extremal black hole mimickers: geometry, stability, and long-delay signal trains
AU - Sergey N Solodukhin
PY - 2026
DA - 2026/10/16
PB - HAL
DO - 10.48550/arxiv.2610.11664
UR - https://hal.science/hal-05835182v1
AB - We present a spacetime that serves as a horizonless mimicker of extremal black holes. Unlike previously studied mimickers of black holes with non-degenerate horizons, whose geometries are of the wormhole type and consist of two asymptotically flat regions connected by a very long throat, the mimicker of an extremal black hole possesses a single asymptotically flat region at one end and an infinitely long throat at the other. In the throat region, the spacetime approaches the direct-product geometry M_1,1 × S^2, where M_1,1 is two-dimensional Minkowski spacetime and S^2 is the two-sphere. We investigate scalar-field dynamics and the fate of the Aretakis instability. Although Aretakis-like modes arise in a local analysis of the throat, they do not lead to a physical instability of the mimicker. A scalar perturbation initially localized in the throat gives rise, at late times, to a sequence of signals with a characteristic separation t_delay∼ 1/λ, where λ≪ 1 is a deformation parameter. This timescale is parametrically larger than the echo time t_echo∼ ln(1/λ) characteristic of non-extremal black-hole mimickers. We refer to this sequence as a {\it long-delay signal train}. Geometrically, the periodicity of the long-delay signals is associated with periodic geodesics on S^2. We then extend the construction to extremal Kerr. In this case, the throat region approaches a generalized product geometry involving M_1,1 and a two-dimensional surface Σ_2. The corresponding signals are expected to form a quasi-periodic signal train, reflecting the quasi-periodic geodesic motion on Σ_2. We also comment on the generalization to wormhole mimickers of non-extremal black holes and on the implications of these results for unitarity in the context of the AdS/CFT correspondence.
ER -